Independent Degrees Of Freedom Research Articles

Counterrotation of magnetic beads in spinning fields.

A magnetic stirrer, an omnipresent device in the laboratory, generates a spinning magnetic dipolelike field that drives in a contactless manner the rotation of a ferromagnetic bead on top of it. We investigate here the surprisingly complex dynamics displayed by the spinning magnetic bead emerging from its dissipatively driven, coupled translation and rotation. A particularly stunning and counterintuitive phenomenon is the sudden inversion of the bead's rotational direction, from corotation to counterrotation, acting seemingly against the driving field, when the stirrer's frequency surpasses a critical value. The bead counterrotation effect, experimentally described by Chau etal. [J. Magn. Magn. Mater. 476, 376 (2019)JMMMDC0304-885310.1016/j.jmmm.2018.12.073], is here comprehensively studied, with numerical simulations and a theoretical approach complementing experimental observations.

Dirac branes for Dirichlet branes: Supergravity actions

Nontrivial Bianchi identities with local magnetic sources are solved by recognizing that gauge potentials are sections rather than globally defined functions, but properly accounting for the source degrees of freedom requires a modification of the field strength. Following work by Teitelboim and by Cariglia and Lechner, we extend Dirac's string formalism for monopoles to D-branes in type IIA and IIB string theory. We give novel derivations of brane-induced Chern-Simons terms in the supergravity actions, including a prescription for integrating over potentials in the presence of magnetic sources. We give a noncovariant formulation of the IIB theory, keeping only the independent degrees of freedom of the self-dual 4-form potential. Finally, it is well-known that D8-branes source the mass parameter of IIA supergravity; we show that the additional couplings of the massive IIA supergravity, including on other D-brane worldvolumes, are a consequence of the corresponding Dirac branes.

Linear and nonlinear dynamical analysis of a Crane model

Abstract:This paper deals with the dynamical analysis of a crane model. Truss finite elements are used to discretize the suspending chains with the so called updated Lagrangian description. This nonlinear model is regarded to be the best approximation to which linear models are compared. The inertia and independent degrees of freedom are also taken into consideration by linear models. The goal is to find a linear model, which can be used as an observer in antisway control of a crane.

A Micromorphic Beam Theory for Beams with Elongated Microstructures

A novel micromorphic beam theory that considers the exact shape and size of the beam’s microstructure is developed. The new theory complements the beam theories that are based on the classical mechanics by modeling the shape and size of the beam’s microstructure. This theory models the beam with a microstructure that has shape and size and exhibits microstrains that are independent of the beam’s macroscopic strains. This theory postulates six independent degrees of freedom to describe the axial and transverse displacements and the axial and shear microstrains of the beam. The detailed variational formulation of the beam theory is provided based on the reduced micromorphic model. For the first time, the displacement and microstrain fields of beams with elongated microstructures are developed. In addition, six material constants are defined to fully describe the beam’s microscopic and macroscopic stiffnesses, and two length scale parameters are used to capture the beam size effect. A case study of clamped-clamped beams is analytically solved to show the influence of the beam’s microstructural stiffness and size on its mechanical deformation. The developed micromorphic beam theory would find many important applications including the mechanics of advanced beams such as meta-, phononic, and photonic beams.

An improved crack-tip element treatment for advanced FEMs

This paper presents an improved treatment for those advanced FEMs that use stresses in the crack-tip element for evaluation crack propagation condition. We show that the common treatment of obtaining crack-tip displacements using simple interpolation from the edge of the crack-tip element is inaccurate and is responsible for the jagged jump and unwarping behavior (JJU) frequently reported in literature. In this study we propose a more accurate treatment by introducing an element node with independent degree of freedom (DoF) to enrich the crack-tip element. We show that the proposed approach can relieve the stiffness overestimation of the crack-tip element without disrupting the standard element interpolation process. Results of numerical examples demonstrate that the improved treatment can greatly improve the stress shielding phenomenon and effectively reduce the JJU in load-displacement curves.

Independent degrees of freedom in two-dimensional materials

In hexagonal two-dimensional (2D) materials such as graphene, hexagonal boron nitride, or transition metal dichalcogenides, electrons possess intrinsic degrees of freedom (DOFs): sublattice pseudospin, spin, and valley. Independent polarization of the DOFs for carrying information can be harnessed in future semiconductor industry. Here we propose a general Hamiltonian based on the Haldane model with spin-orbit coupling (SOC) which realizes the independence of all the DOFs that can tune optical absorption spectra as a function of the SOC. The present result suggests a new 2D material or a new 2D electronic device which offers any combination of pseudospintronics, spintronics, and valleytronics applications.

A multilevel hypernetworks approach to capture properties of team synergies at higher complexity levels

Previous work has sought to explain team coordination using insights from theories of synergy formation in collective systems. Under this theoretical rationale, players are conceptualised as independent degrees of freedom, whose interactions can become coupled to produce team synergies, guided by shared affordances. Previous conceptualisation from this perspective has identified key properties of synergies, the measurement of which can reveal important aspects of team dynamics. However, some team properties have been measured through implementation of a variety of methods, while others have only been loosely addressed. Here, we show how multilevel hypernetworks comprise an innovative methodological framework that can successfully capture key properties of synergies, clarifying conceptual issues concerning team collective behaviours based on team synergy formation. Therefore, this study investigated whether different synergy properties could be operationally related utilising hypernetworks. Thus, we constructed a multilevel model composed of three levels of analysis. Level N captured changes in tactical configurations of teams during competitive performance. While Team A changed from an initial 1-4-3-3 to a 1-4-4-2 tactical configuration, Team B altered the dynamics of the midfielders. At Level N + 1, the 2 vs. 1 (1 vs. 2) and 1 vs. 1 were the most frequently emerging simplices, both behind and ahead of the ball line for both competing teams. Level N + 2 allowed us to identify the prominent players (a6, a8, a12, a13) and their interactions, within and between simplices, before a goal was scored. These findings showed that different synergy properties can be assessed through hypernetworks, which can provide a coherent theoretical understanding of competitive team performance.

Self-dual forms: action, Hamiltonian and compactification

It has been shown that, by adding an extra free field that decouples from the dynamics, one can construct actions for interacting 2n-form fields with self-dual field strengths in 4n+ 2 dimensions. In this paper we analyze canonical formulation of these theories, and show that the resulting Hamiltonian reduces to the sum of two Hamiltonians with independent degrees of freedom. One of them is free and has no physical consequence, while the other contains the physical degrees of freedom with the desired interactions. For the special cases of chiral scalars in two dimensions and chiral two form fields in six dimensions, we discuss compactification of these theories respectively on a circle and a two dimensional torus, and show that we recover the expected properties of these systems, including S-duality invariance in four dimensions.

Advanced DSP for Coherent Optical Fiber Communication

In this paper, we provide an overview of recent progress on advanced digital signal processing (DSP) techniques for high-capacity long-haul coherent optical fiber transmission systems. Not only the linear impairments existing in optical transmission links need to be compensated, but also, the nonlinear impairments require proper algorithms for mitigation because they become major limiting factors for long-haul large-capacity optical transmission systems. Besides the time domain equalization (TDE), the frequency domain equalization (FDE) DSP also provides a similar performance, with a much-reduced computational complexity. Advanced DSP also plays an important role for the realization of space division multiplexing (SDM). SDM techniques have been developed recently to enhance the system capacity by at least one order of magnitude. Some impressive results have been reported and have outperformed the nonlinear Shannon limit of the single-mode fiber (SMF). SDM introduces the space dimension to the optical fiber communication. The few-mode fiber (FMF) and multi-core fiber (MCF) have been manufactured for novel multiplexing techniques such as mode-division multiplexing (MDM) and multi-core multiplexing (MCM). Each mode or core can be considered as an independent degree of freedom, but unfortunately, signals will suffer serious coupling during the propagation. Multi-input–multi-output (MIMO) DSP can equalize the signal coupling and makes SDM transmission feasible. The machine learning (ML) technique has attracted worldwide attention and has been explored for advanced DSP. In this paper, we firstly introduce the principle and scheme of coherent detection to explain why the DSP techniques can compensate for transmission impairments. Then corresponding technologies related to the DSP, such as nonlinearity compensation, FDE, SDM and ML will be discussed. Relevant techniques will be analyzed, and representational results and experimental verifications will be demonstrated. In the end, a brief conclusion and perspective will be provided.

Affine Killing vector fields on homogeneous surfaces with torsion

Many extensions of general relativity are based on considering metric and affine structures as independent properties of spacetime. This leads to the possibility of introducing torsion as an independent degree of freedom. In this article we examine the effects of torsion on the affine Killing vectors of two-dimensional manifolds. We give a complete description of the Lie algebras of affine Killing vector fields on homogeneous surfaces. This can be used in the search of non-metrizable surfaces of interest.

Numerical simulation of precast RC beams joined by mechanical Connectors using the finite element method

ABSTRACTThe finite element method is used in this study to propose a mathematical model to simulate the structural response of Precast RC beams joined by mechanical connectors distributed in the cross section of the beam according to a new configuration proposal. The model is based on the theory of Continuum Mechanics. Each reinforcement bar is represented independently, and the behavior of the concrete-reinforcement interface is modelled using two different approaches. The first one considers perfect adhesion in the interface, and in the second steel-concrete sliding is modelled using independent degrees of freedom at the reinforcement nodes. The cracking response of the beams is modelled using discrete and smeared crack models for concrete fracture representation of cracks. The joint section is modelled using interface zero-thickness elements and a discrete representation of the crack already formed at the joint. The comparison of experimental and analytical results shows good agreement.

Artificial Soft Cilia with Asymmetric Beating Patterns for Biomimetic Low‐Reynolds‐Number Fluid Propulsion

AbstractIn nature, liquid propulsion in low‐Reynolds‐number regimes is often achieved by arrays of beating cilia with various forms of motion asymmetry. In particular, spatial asymmetry, where the cilia follow a different trajectory in their effective and recovery strokes, is an efficient way of generating flow in low Reynolds regimes. However, this type of asymmetry is difficult to mimic and control artificially. In this paper, an artificial soft cilium that comprises two pneumatic actuators that can be controlled individually is developed. These two independent degrees of freedom allow for the first time adjustment and study of spatial asymmetry in the cilium's beating pattern. Using low‐Reynolds‐number flow measurements, it is confirmed that spatial asymmetry allows for the generation of fluid propulsion. These two‐degree‐of‐freedom soft cilia provide a platform to study ciliary fluid transport mechanisms and to mimic biologic viscous propulsion.

Is the Human Brain Capable of Controlling Seven Degrees of Freedom?

BackgroundConventional rigid laparoscopic instruments offer five degrees of freedom (DOF). Robotic instruments add two independent DOFs allowing unconstrained directional steering. Several nonrobotic instruments have been developed with the additional DOFs, but with these devices, surgeon's wrist movements are not intuitively transmitted into tip movements. In this study, a new articulated instrument has been evaluated. The aim of the study was to compare learning curves and performances of conventional laparoscopic instruments, the da Vinci system and Steerable devices in a crossover study. Materials and methodsA total of 16 medical students without any laparoscopic experience were trained for 27 h to operate all of a rigid, a robotic, and a new Steerable instrument in a random order. Learning curves and ultimate experience scores were determined for each instrument. Strain in wrist and shoulders was assessed with a visual analog score. ResultsPerforming the suturing task with rigid and robot instruments required 4 h of training, compared with 6 h to master the Steerable instrument. After 9 h of training with each instrument, completing the complex suturing pattern required 662 ± 308 s with rigid instruments, 279 ± 90 s with the da Vinci system, and 279 ± 53 s with the Steerable instrument. Pain scores were significantly higher after using the rigid instruments compared with the Steerable instruments. ConclusionsTransmission of torque and the presence of additional two DOFs in combination with reduced crosstalk significantly improved the instrument dexterity where the Steerable platform is concerned. Although the learning curve is longer, once mastered, it provides enhanced surgical freedom.

Multibody dynamical modeling of the FPSO soft yoke mooring system and prototype validation

The Soft Yoke Mooring System (SYMS) is a single point mooring system for shallow water. It is composed of a mooring framework, mooring legs, yoke, and single point, and is located at the Floating Production Storage and Offloading (FPSO) through 13 hinge joints, such as universal joints and thrust bearings. Mooring restoring force, motions and postures of mooring components, and mechanical behaviors of hinge joints are major criteria for the structural design of the SYMS. Aiming at the difficulties of the multibody dynamics in traditional design of the SYMS, a multi-body dynamic mathematical modeling with seven independent degrees of freedom (DOFs) which is applicable to prototype field engineering was developed in this study. The proposed mathematical modeling of the SYMS multibody dynamic system has several advantages: 1. Internal tribological behaviors in hinge joints are considered within the presented multibody dynamics model to illustrate the good dynamic effects of the SYMS. 2. The multibody dynamic model can be applied in field service. Correctness and feasibility of the proposed multibody dynamic simulation method for describing motions and postures of hinges and single-body were validated by the prototype monitoring data. 3. The horizontal restoring force of the SYMS was calculated according to field measurement data. The motion state of each single body and internal stress distributions at each hinge joint in the SYMS are given. 4. The multibody dynamics calculation program can be directly used for the real-time monitoring of mechanical behaviors of the SYMS under the service state. The simulated results can provide real-time guarantee for safety alarming of the system. The vulnerability of the mooring system in service was evaluated based on long-term monitoring data analysis.

Direct measurement of Lighthill's energetic efficiency of a minimal magnetic microswimmer.

The realization of artificial microscopic swimmers able to propel in viscous fluids is an emergent research field of fundamental interest and vast technological applications. For certain functionalities, the efficiency of the microswimmer in converting the input power provided through an external actuation into propulsive power output can be critical. Here we use a microswimmer composed by a self-assembled ferromagnetic rod and a paramagnetic sphere and directly determine its swimming efficiency when it is actuated by a swinging magnetic field. Using fast video recording and numerical simulations we fully characterize the dynamics of the propeller and identify the two independent degrees of freedom which allow its propulsion. We then obtain experimentally the Lighthill's energetic efficiency of the swimmer by measuring the power consumed during propulsion and the energy required to translate the propeller at the same speed. Finally, we discuss how the efficiency of our microswimmer could be increased upon suitable tuning of the different experimental parameters.

Spatiotemporal description of long-delayed systems: Ruling the dynamics

The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their identification as equivalent space and time variables does not lead to a correct dynamical rule. We introduce a new framework for a proper description of the dynamics in the thermodynamic limit, providing a general avenue for the treatment of long-delayed systems in terms of partial differential equations. Such scheme is generic and does not depend on the vicinity of a super-critical bifurcation as required in previous approaches. We discuss the general validity and limit of this method and consider the exemplary cases of long-delayed excitable, bistable and Landau systems.

Slave rotor approach to exciton condensation in a two-band system

We have studied exciton formation and condensation in an extended Falicov–Kimball model, going beyond the weak coupling approach, employing a semi-analytical technique: the slave-rotor mean-field theory (SRMF). In this essentially strong coupling theory, charge and spin (or orbital/pseudospin) degrees are treated as independent degrees of freedom, coupled by a local constraint. Using a two-site-extension of SRMF, we capture the effective many body scale beyond conventional mean-field theory. While the formation of excitons is favoured by the interband hybridization , it is strongly influenced by the on-site Coulomb interaction . Beyond a critical hybridization, there is condensation of excitons, leading to a transition from a metal to an excitonic insulator phase. Moreover, the behaviour of excitonic averages differs from the usual Hartree–Fock mean-field theory. Low- results show that excitonic order parameter (Δ) is continuous across the transition both for single as well as two-site approximation, changing to weakly first order one at intermediate for the later. The large- limit shows a continuous transition for two-site analysis but remains first order in the single-site approximation. The slave rotor theory gives a mixed state of excitons and metal in both the analyses. We have also checked the effect of intersite correlation and localized band hopping on the exciton condensation.

Thermo-mechanical stability analysis of functionally graded shells

In this paper, the thermo-elastic nonlinear analysis of various Functionally Graded (FG) shells under different loading conditions is studied. A second-order isoparametric triangular shell element is presented for this purpose. The element is six-noded, and each node has all six independent degrees of freedom in space. It should be added, the first-order shear deformation theory is induced. Furthermore, Voigt’s model is adopted to define the FG material properties, which are considered to change gradually from one surface to another. The critical temperature is predicted. Both the pre-buckling and post-buckling equilibrium paths are traced. Since the linear eigenvalue analysis leads to wrong responses in the problems with strong nonlinearity, the suggested procedure is performed based on the FEM and more exact estimations are achieved using equilibrium path.

Design and Analysis for a Three-Rotational-DOF Flight Simulator of Fighter-Aircraft

Most of researchers focused on traditional six degrees of freedom (DOF) Stewart flight simulator, which can not be adaptive in fighter-aircraft flight simulator. A three rotational DOF flight simulator of fighter-aircraft based on double parallel manipulator and hybrid structure is presented. The flight simulator is composed of two identical 3-RRS (revolute-revolute-spherical) spherical parallel manipulators and one cabin, called Twins. The cabin has an additional independent DOF for 360° continuous rotation, so it can be applied as a flight simulator for a fighter-aircraft to achieve spin maneuvering. Because of the introduction of the hybrid structure and double parallel manipulator of the mechanism, the redundancy exists with respect to both kinematics and actuation. Kinematics is carried out and Jacobian matrix is established by means of screw theory. The inverse kinematics is given out by the analytical method. 64 groups inverse solutions are showed in a table by permutation. Forward kinematics is solved by an effectively numerical method. The forward numerical method is realized based on the analytically inverse kinematics and Jacobian matrix. The numerical examples show that the forward numerical method can be used in real-time control. The rolling motion is considered in forward kinematics and a numerical example is given out. The proposed flight simulator can spin and there are three rotational DOF with a hybrid structure so that the novel flight simulator can be used in the field of the fighter-aircraft for pilots to train.

Gravity until equipartition of relativistic kinetic energies

Einstein‘s relativistic mechanics can describe the low speed transport of variable internal and translation energies through two independent degrees of freedom while Newton‘s model of cold masses always operates only with one degenerated degree for these kinetic energies. Despite similar mathematics with Newton, Einstein‘s low speed physics for the spatial transport of variable internal heat and kinetic energy of ordered translations differs essentially from the classical physics of constant masses. Gravity of mechanical bodies with internal relativistic heat originates from the universal tendency of kinematic energies to their dynamical equipartition over available degrees of freedom. The free fall deceleration in extreme fields is followed by the accelerated takeoff and by further oscillations around the kinematic energy equilibrium.